After back-up arrived, "they were subject to heavy shooting from several locations inside the Yemeni border," sparking a firefight, it said.

Ageeli is one of the most senior Saudi officers killed since March when the kingdom formed an Arab coalition to fight Shia Houthi rebels in Yemen.

Meanwhile, the coalition air strikes killed three children and fighting on the ground between the rebels and the pro-government fighters in the southern province of Taiz killed at least 10 people, Yemen's medical officials said on Friday.

The Houthis, who control much of Taiz province, have over the past weeks laid siege in the to the city of Taiz, Yemen's third-largest, where pro-government troops have set up camp, independent security officials said. Friday's ground attack was an attempt to re-enter the city, the officials said.

All of the officials spoke on condition of anonymity because they were not authorised to talk to reporters.

"It is almost impossible to send aid to Taiz," said Hassan Boucenine of the Geneva-based aid group Doctors Without Borders, also known as Medecins Sans Frontieres or MSF. "Until a couple of weeks ago, you could send some during the day, but not any more."

More than 2,100 civilians have been killed, according to UN estimates.

Yemen's fighting pits the rebels, known as Houthis, and forces loyal to former President Ali Abdullah Saleh against the Saudi-backed and internationally recognised government forces as well as southern separatists, local militias and Sunni rebels.